INC 112 Basic Circuit Analysis Week 13 Frequency Response

What is the change of vL(t) when the frequency of the voltage source change?

ω |vL| (magnitude) A

Log ω |vL| (magnitude) Log scale of frequency A

Linear Scale & Log Scale Linear Scale Log Scale

What is the frequency response of vc(t) Log ω |vc| (magnitude) A

Input & Output System Input Output Input is usually what we can control. Output is usually what we are interested in.

What is the frequency response of vc(t) Input = voltage source Output = vc(t)

Frequency Domain Frequency domain is another point of view of things in the world. Some analysis are easier done in frequency domain than time domain.

Metaphor of Frequency Domain (1,1,1) (2,-3,0) Time Domain Frequency Domain

Time Domain Frequency Domain

Transfer Function Transfer function = ratio of output and input in frequency domain System H(s) System H(s) Input Output U(s)Y(s) Transfer function Note: Transfer function describes characteristic of a system.

Example: Obtaining Transfer Function input is v(t) output is vc(t)

Change all components to Phasor (frequency domain)

Kirchoff’s Voltage Law

Transfer function

Frequency Response System Input Output Freq 10Hz Amplitude = 1Phase = 0 Freq 100Hz Amplitude = 1Phase = 0 Freq 800Hz Amplitude = 1Phase = 0 Freq 10Hz Amplitude = 0.96 Phase = 12 Freq 100Hz Amplitude = 0.82 Phase = 44 Freq 800Hz Amplitude = 0.53 Phase = 56

Frequency Response Plot Note: log frequency and log magnitude Magnitude Phase

The HP 35670A Dynamic Signal Analyzer obtains frequency response data from a physical system.

Fourier Series “Any periodic signal can be written in the sum of sine wave signals at different frequency.”

Filter Log ω |vc| (magnitude) We want to get rid of the signal 3sin(9t) ω=5ω=5 Cut-off frequency

Example Find vc(t) Use superposition to consider the effect of two different frequencies

For 2sin(t)

For 3sin(9t)

Finally, we add vc(t) from both frequencies

Power Line Systems 3 phases systems have three wire called “line” which are sine wave with phase shift 120 from each other Power Plant Line 1 Line 2 Line 3 3 phases, 3 wires

Power Plant Line 1 Line 2 Line 3 3 phases, 4 wires Neutral L1-N = 220Vrms, L2-N = 220Vrms L3-N = 220Vrms L1-L2 = 381Vrms,L2-L3 = 381Vrms,L1-L3 = 381Vrms

Star Connection ( Y-connection) Load Each load get 220 Vrms

Delta Connection ( Δ-connection) Load Each load get 381 Vrms